The simplest theoretical description of ferromagnetism is called the Ising model. This model was invented by Wilhelm Lenz in 1920: it is named after Ernst Ising, a student of Lenz who chose the model as the subject of his doctoral dissertation in 1925. The aim of this project is introduce an Ising model and investigate the properties of a two dimensional ferromagnet with respect to its magnetization and energy at varying temperatures. The observable are evaluated as an application of Monte Carlo techniques. Key background is given about the relevance and effectiveness of this stochastic approach and in particular the applicability of the Metropolis-Hastings algorithm in FORTRAN programming language. - View it on GitHub